Winter wk 1 – Thus.6.Jan.05 Calculus Ch.5: Integration –5.1: How do we measure distance traveled? –5.2: The definite integral If we have time, Physics.

Winter wk 1 – Thus.6.Jan.05

• Calculus Ch.5: Integration– 5.1: How do we measure distance traveled?

– 5.2: The definite integral

• If we have time, Physics Ch.22 from yesterday: Electric fields

• Seminar in CAL tonight – come at 5:30

Energy Systems, EJZ

Calculus Ch.5: Integration

5-1: How do we measure distance traveled?

• Thought experiment: how far does a car go?– Estimate distance traveled in each time interval

• Making distance estimates precise– Take smaller and smaller time intervals

• Conceptests

• Practice problems #1, 2, 4, 5, 6, 10, 14

5-1: Estimating distance traveled

Speed = distance/time, so Distance = ________

Plot speed vs time

Estimate distance for each interval

Area of (speed*time) segments

Fig.5.1: LH sum = underestimate,

RH sum = overestimate

Practice problems # 2, 4, 10

Calc Ch.5-1 Conceptest 1

Calc Ch.5-1 Conceptest 1 soln

Calc Ch.5-1 Conceptest 2

5.1 #2

5.1 #4

5.1 #10

Calculus Ch.5.2: Definite integral

• Sums using Sigma notation

• Taking the limit to get the definite integral

• Definite integral as an Area

• Riemann sums

• Conceptests

• Practice problems #1, 2, 4, 16, 20, 22, 28

5.2: Sums using sigma notation

Time interval = total time/number of steps

t = (b-a) / n

Speed at a given time = f(t)

Area of speed*time interval = distance = f(t)*t

Total distance traveled = sum over all intervalsn

tot 1 2 n ii=0

x f(t ) t + f(t ) t +...+ f(t ) t = f(t ) t

5.2: Definite integral

Precise calculation of total distance traveled xtot

needs infinitesimally small time intervals,

so take the limit as t 0, that is,

an infinite number of tiny intervals: n

Practice problems #1, 2, 4, 16

n

tot ini=0

x = lim f(t ) t ( )b

a

f t dt

Calc Ch.5-2 Conceptest 1

Calc Ch.5-2 Conceptest 1 soln

Calc Ch.5-2 Conceptest 2

(Just consider A1)

Ch.5-2 #1

Ch.5-2 #4

Physics Ch.22: Electric Field

22-3: Electric field E maps the direction and strength of the force F (Q1, #1, 2)

22-4: Field due to a point charge (Q2, 5, #4, 11, )

22-8: Point charge can be accelerated by an electric field (Q8, #38, 39, 49)

Compare to gravity: #75, 85 (42)

E field maps electric force

22-3: Electric field E maps the direction and strength of the force F (Q1, #1, 2)

Field due to a point charge

22-4: Field due to a point charge (Q2, 5, #4, 11, )

If the Earth’s electric field is 150 N/C near the surface, what is the charge Q on the Earth?

What is the charge density (=Q/area)?

22-8 E field can accelerate chargesQ8, #38, 39, 49

Compare E to gravity: #75, 85 (42) A spherical water droplet is suspended in a cloud with E=462 N/C (a) What is Fg on the drop? (b) How many excess electrons does it have?